2026 IGCSE Additional Mathematics May/June 0606/21 Q8

In this question lengths are in centimetres and angles are in radians.

The diagram shows a circle, centre \(C\), radius 10.

The points \(A\) and \(B\) lie on the circumference of the circle.

The point \(P\) is such that \(CBP\) is a straight line.

The line \(BP\) has length \(x\).

The line \(AP\) is a tangent to the circle at \(A\).

Angle \(ACB\) is \(\theta\).

The perimeter of the triangle \(APC\) is 38.

1. Show that the value of \(\theta\) is 0.885 radians correct to 3 decimal places.[6]
2. Find the length of the arc \(AB\).[1]
3. Find the area of the sector \(ACB\).[1]